572 research outputs found
Using Program Synthesis for Program Analysis
In this paper, we identify a fragment of second-order logic with restricted
quantification that is expressive enough to capture numerous static analysis
problems (e.g. safety proving, bug finding, termination and non-termination
proving, superoptimisation). We call this fragment the {\it synthesis
fragment}. Satisfiability of a formula in the synthesis fragment is decidable
over finite domains; specifically the decision problem is NEXPTIME-complete. If
a formula in this fragment is satisfiable, a solution consists of a satisfying
assignment from the second order variables to \emph{functions over finite
domains}. To concretely find these solutions, we synthesise \emph{programs}
that compute the functions. Our program synthesis algorithm is complete for
finite state programs, i.e. every \emph{function} over finite domains is
computed by some \emph{program} that we can synthesise. We can therefore use
our synthesiser as a decision procedure for the synthesis fragment of
second-order logic, which in turn allows us to use it as a powerful backend for
many program analysis tasks. To show the tractability of our approach, we
evaluate the program synthesiser on several static analysis problems.Comment: 19 pages, to appear in LPAR 2015. arXiv admin note: text overlap with
arXiv:1409.492
Counterexample-Guided Prophecy for Model Checking Modulo the Theory of Arrays
We develop a framework for model checking infinite-state systems by
automatically augmenting them with auxiliary variables, enabling
quantifier-free induction proofs for systems that would otherwise require
quantified invariants. We combine this mechanism with a counterexample-guided
abstraction refinement scheme for the theory of arrays. Our framework can thus,
in many cases, reduce inductive reasoning with quantifiers and arrays to
quantifier-free and array-free reasoning. We evaluate the approach on a wide
set of benchmarks from the literature. The results show that our implementation
often outperforms state-of-the-art tools, demonstrating its practical
potential.Comment: 23 pages, 1 figure, 1 table, extended version of paper to be
published in International Conference on Tools and Algorithms for the
Construction and Analysis of Systems 202
Interpolant-Based Transition Relation Approximation
In predicate abstraction, exact image computation is problematic, requiring
in the worst case an exponential number of calls to a decision procedure. For
this reason, software model checkers typically use a weak approximation of the
image. This can result in a failure to prove a property, even given an adequate
set of predicates. We present an interpolant-based method for strengthening the
abstract transition relation in case of such failures. This approach guarantees
convergence given an adequate set of predicates, without requiring an exact
image computation. We show empirically that the method converges more rapidly
than an earlier method based on counterexample analysis.Comment: Conference Version at CAV 2005. 17 Pages, 9 Figure
On abstraction refinement for program analyses in Datalog
A central task for a program analysis concerns how to efficiently find a program abstraction that keeps only information relevant for proving properties of interest. We present a new approach for finding such abstractions for program analyses written in Datalog. Our approach is based on counterexample-guided abstraction refinement: when a Datalog analysis run fails using an abstraction, it seeks to generalize the cause of the failure to other abstractions, and pick a new abstraction that avoids a similar failure. Our solution uses a boolean satisfiability formulation that is general, complete, and optimal: it is independent of the Datalog solver, it generalizes the failure of an abstraction to as many other abstractions as possible, and it identifies the cheapest refined abstraction to try next. We show the performance of our approach on a pointer analysis and a typestate analysis, on eight real-world Java benchmark programs
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